Quantifying Tripartite Entanglement in Quantum Information and Technologies

Tripartite entanglement, a fundamental resource in quantum information and technologies, has been extensively studied in recent years. However, quantifying genuine tripartite entanglement (GME) remains an open challenge. Existing measures often fail to meet the required criteria, leading to inconsistent results. In this study, researchers investigate GME for three-qubit pure states using a novel measure, concurrence. They also examine tripartite steering, a crucial aspect of quantum information and technologies, and identify nine potential configurations exhibiting varying steerability across different parameter spaces. The findings have significant implications for the development of quantum technologies.

What is the Significance of Tripartite Entanglement in Quantum Information and Technologies?

Tripartite entanglement, existing in two-party, three-party, or even more-party systems, is a vital resource for quantum information and technologies. To quantify this resource, numerous measures have been developed, including partial norm, entanglement of formation, von Neumann entropy, normalized negativity, concurrence, and others. A key task in quantum information theory involves quantifying the genuine tripartite entanglement (GME). However, GME necessitates two requirements: it must assign a zero value to any product state or biseparate state, and it must assign a positive value to all non-biseparate states.

Most existing measures fail to meet these requirements by either violating requirement I or requirement II. For instance, measures such as the Schmidt measure and global entanglement violate requirement I, while measures like the 3-tangle and generalized negativity violate requirement II. Recently, Xie and Eberly introduced concurrence, offering a novel measure to quantify GME.

We identify nine potential configurations exhibiting varying steerability across different parameter spaces. It is important to highlight that while the state ψ123 exhibits entanglement, steering remains unattainable in a substantial portion of the parameter space.

A key task in quantum information theory involves quantifying the genuine tripartite entanglement (GME) for three-qubit pure states. However, most existing measures fail to meet the genuine criterion by either violating requirement I or requirement II.

Tripartite steering plays a crucial role in quantum information and technologies. It enables us to quantify the steerability of three-qubit pure states under certain measurements based on the uncertainty relations criterion.

This study has significant implications for quantum information and technologies. It highlights the importance of tripartite entanglement and steering in three-qubit pure states, and provides a novel measure to quantify GME.